Reinforcement learning (and, in particular, bandit) algorithms have been and can be used to solve problems other than games, such as
- Recommender systems (actually used in practice by e.g. Netflix or Microsoft)
- Portfolio optimization
- Clinical trials
- Hyper-parameter optimization
- Self-driving cars (although I am not aware of any real self-driving car that uses just reinforcement learning; however, in principle, RL can be used in this context too)
In general, any problem that can be modelled as the maximization of some notion of reward, where you need to interact with some environment (with some states) by taking some actions, can, in principlein principle, be solved by reinforcement learning. Take a look at this pre-print paper (2019) for other applications.
However, note that there are several obstacles that prevent RL algorithms from being widely adopted to solve real-world problems, starting from poor sample complexity (i.e. they require many samples to reach a good performance) or the partial inability to evaluate their performance online without affecting the users.